Page 1 of 2
ACTIVITY 8.5
Using Technology
Graphing Calculator Activity for use with Lesson 8.5
Graphing
Logarithmic Functions
You can use a graphing calculator to graph logarithmic functions simply by
using the
or
key. To graph a logarithmic function having a base
other than 10 or e, you need to use the change-of-base formula to rewrite
the function in terms of common or natural logarithms.
EXAMPLE
Use a graphing calculator to graph y = log2 x and y = log2 (x º 3) + 1.
SOLUTION
INT
STUDENT HELP
NE
ER T
KEYSTROKE
HELP
See keystrokes for
several models of
calculators at
www.mcdougallittell.com
1 Rewrite each function in terms of common logarithms.
y = log2 x
log x
log 2
= y = log2 (x º 3) + 1
log (x º 3)
log 2
= + 1
2 Enter each function into a graphing calculator.
Y1=(log X)/(log 2)
Y2=(log (X-3))/
((log 2)+1)
Y3=
Y4=
Y5=
Y6=
Although the calculator will correctly
evaluate the function without parentheses,
you can include them for clarity.
3 Graph the functions.
The graph of y = log2 x passes
through (1, 0), and the line
x = 0 is a vertical asymptote.
The graph of y = log2 (x – 3) + 1
passes through (4, 1), and the line
x = 3 is a vertical asymptote.
EXERCISES
Use a graphing calculator to graph the function. Give the coordinates of a point
through which the graph passes, and state the vertical asymptote of the graph.
1. y = log3 x
2. y = log9 x
3. y = log4 x
4. y = log7 x
5. y = log5 x
6. y = log11 x
7. y = log5 (x º 2)
8. y = log4 (x + 1)
9. y = log2 (x º 5) º 3
10. y = log4 (x º 7) + 9
11. y = log5 (x + 2) + 6
12. y = log7 (x º 4) + 4
13. Compare the domains of the graphs of y = log x and y = log |x|.
500
Chapter 8 Exponential and Logarithmic Functions